Question

find the distance between the two points. round your answer to the nearest tenth.

1. ( a(-3, 3), b(3, -3) ) 13. ( a(-2, -6), b(-2, -2) )
2. (\boxed{})
3. (\boxed{})

options: ( mleft(1\frac{3}{4}, 2\frac{1}{8}
ight) ), ( m(6, 1) ), ( m(0, 2.5) ), ( m(1.1, -0.1) ), ( m(3, 1) ), ( m(2.5, 10) ), ( m(5, -6) ), ( b(3, 8) ), ( b(-3, 2) ), ( b(7, 14) ), ( b(6, 0) ), ( 4 ), ( 5 ), ( 5.3 ), ( 5.7 ), ( 6.7 ), ( 7.2 ), ( 7.6 ), ( 8 ), ( 8.5 ), ( 9.2 ), ( 11.7 ), ( 12 ), ( 14 ), ( 26.9 )

Explanation:

Step1: Use distance formula for Q12

The distance formula between points $(x_1,y_1)$ and $(x_2,y_2)$ is $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$.
For $A(-3,3), B(3,-3)$:
$$d=\sqrt{(3-(-3))^2+(-3-3)^2}=\sqrt{(6)^2+(-6)^2}=\sqrt{36+36}=\sqrt{72}$$

Step2: Calculate and round Q12

$\sqrt{72}\approx8.485$, rounded to nearest tenth is $8.5$.

Step3: Use distance formula for Q13

For $A(-2,-6), B(-2,-2)$:
$$d=\sqrt{(-2-(-2))^2+(-2-(-6))^2}=\sqrt{(0)^2+(4)^2}=\sqrt{0+16}=\sqrt{16}$$

Step4: Calculate and round Q13

$\sqrt{16}=4$, which is already a whole number.

Answer:

1. 8.5
2. 4